Alerts are a list of alert rules that is displayed in the back end. You may configure the default behavior of the alerts that will be inherited by the profiles on the site.
In a nutshell, you will be able to configure if the user should receive
System Notifications or
E-mail Notifications or both.
System notifications are notifications that appears on the notification bar below.
E-mail notification allows user's to receive e-mails when specific action occurs on his profile.